Combining hierarchy and energy for drawing directed graphs

Liran Carmel*, David Harel, Yehuda Koren

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


We present an algorithm for drawing directed graphs which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

Original languageAmerican English
Pages (from-to)46-57
Number of pages12
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
StatePublished - Jan 2004
Externally publishedYes


  • Directed graph drawing
  • Fiedler vector
  • Force directed layout
  • Hierarchy energy
  • Minimum linear arrangement


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